Fractal Pore-Scale Model for Effective Thermal Conductivity of Multiscale Unsaturated Porous Media

Accurate prediction of effective thermal conductivity (ETC) is crucial in thermally enhanced oil recovery (TEOR) for unconventional reservoirs. However, the multiscale structures and multiphase media of unconventional reservoirs challenge the ETC prediction. A novel pore-scale physical model for ETC of multiscale unsaturated porous media is developed by using series-parallel thermal-electrical analogy, where the size distribution of pores and rough elements as well as tortuous flow paths are characterized by fractal geometry. The proposed fractal model shows acceptable agreement with the experimental results. It is found that the increment of tortuosity induces an increase in the thermal resistance of the series part and reduces the ETC accordingly. The rough surface and Knudsen effect can enhance and reduce the ETC, respectively. The present explicit analytical expression for ETC provides a fast and effective way to predict the ETC of unconventional reservoirs, and it also sheds light on the heat conduction mechanisms of multiscale unsaturated porous media.